1. Technical Field
The present invention generally relates to a tracking system for tracking a moving signal source and, more particularly, to a tracking system for tracking an inclined satellite.
2. Description of Related Art
Communications satellites most often orbit the earth in a geostationary orbit. This geostationary orbit is a circular orbit lying in the equatorial plane of the earth at 35,785.6 kilometers (22,247 miles) above the earth's surface at its equator. A satellite placed in such an orbit will have the same angular velocity as the angular velocity of the surface of the earth below. Thus, each satellite appears in one fixed orbital slot (or "station") in the sky. A fixed antenna may be permanently aimed at a targeted geostationary satellite.
Various forces act to perturb the orbit of a satellite in a geostationary orbit. The gravitational attraction of the moon and the sun perturb the orbit in a north-south direction and the radiation force of sunlight and asymmetries in the earth's gravitational field perturb the orbit in an east-west direction. By using thrusters, the satellite can be pushed back to its assigned station to counteract these perturbing forces. This process is known as stationkeeping. Predetermined limits are generally set which define how close a satellite must be kept to its assigned station. FIG. 1 depicts a "stationkeeping box" for a geostationary satellite at 30.0.degree. W longitude. In accordance with the stationkeeping box of FIG. 1, the satellite longitude may vary from 29.9.degree. to 30.1.degree. W longitude and the satellite latitude may vary from 0.1.degree. S to 0.1.degree. N latitude. Since, at present, there is no way to refuel a satellite, the amount of propellant for the thrusters determines how long a satellite can be maintained within its stationkeeping box. Moreover, it takes five to ten times more propellant to correct for north-south variations than for east-west variation. Consequently, inclined orbit operations in which north-south stationkeeping is stopped have allowed satellite operators to extend the useful life of geostationary communications satellites. FIG. 2 is a diagram illustrating how a satellite's orbit becomes inclined and what effects it has on the observed satellite motion. It can be seen that for the entire day, the sun and moon pull on a geostationary satellite in a direction tending to align the satellite with their orbits. With no north-south stationkeeping, the satellite's orbit is continuously pulled away from its geostationary orbit and becomes "inclined" with respect to the equatorial plane of the earth. A satellite in an inclined orbit appears to be above its equatorial position for one half the earth's rotation and below its equatorial position for the other half.
If the orbit becomes inclined with respect to the celestial equator, the satellite appears to move in a pattern that repeats with each rotation of the earth (i.e., once every sidereal day or 23 hours, 56 minutes, and 4.1 seconds). For low inclinations (approximately 1.5.degree. or less), the apparent satellite motion resembles an ellipse. As the satellite inclination increases, the satellite's apparent motion becomes a figure-8. FIG. 3 shows the topocentric motion of the satellite GSTAR III in celestial latitude and longitude. GSTAR III has an inclination of approximately 6.2.degree.. The figure-8 of FIG. 3 is the pattern an observer would see if the observer was on the equator at 267.degree. E longitude. The equations that yield the approximation of this motion may be found, for example, in Pritchard et at., "Satellite Communication Systems Engineering", 2nd ed., Prentice-Hall, N.J. (1993). An observer viewing the satellite from the earth's equator and on the same longitude meridian as the nominal longitude of the satellite sees a smooth and symmetric ellipse or figure-8. An observer that views the satellite from a position not at the equator sees distorted apparent motion. A simple figure-8 equation cannot model the apparent motion because of distortion in the apparent motion of the satellite; normal drift of the satellite; regular station-keeping motion of the satellite; and because the figure-8 pattern only appears for higher inclinations. FIG. 4 shows the apparent motion of GSTAR III as viewed from 275.85.degree. E longitude and 33.94.degree. N latitude. The pattern is recognizable as a figure-8, but simple equations no longer describe the motion.
When inclined orbit satellites are used, an earth station antenna must be able to track the dally movements of the satellites. To implement such tracking, various tracking techniques have been implemented. Low-cost satellite tracking systems frequently use a step-track algorithm to track an inclined satellite. A step-track algorithm automatically finds the antenna position at which the strength of a received beacon signal is maximum. In general, the step-track algorithm causes the antenna to execute excursions about some nominal position. The signal strength is sampled during the excursions and the antenna is moved in the direction of the increasing signal strength. This scanning process is repeated until a stop criterion, indicating that the antenna has found the peak signal, is met. The scanning process is re-initiated based on (1) regular intervals determined by a time threshold value; (2) detections of the signal strength dropping below a specified level; or (3) a combination of both.
A step-track algorithm cannot, however, function if the tracking system loses the beacon signal. Thus, a method of using collected data to predict positions of the satellite is required to follow the satellite when tracking information such as a beacon signal is not available. One method used is to store satellite positions in a so-called park table each time the system peaks the antenna on the satellite signal. The tracking system creates and saves the park table over a period of one sidereal day. This method, called memory or program track, uses the park table to predict satellite locations over each succeeding sidereal day. An interpolation method is used to predict positions between sample times. Program track suffers from several disadvantages. First, the data becomes inaccurate as its age increases. Second, since the tracking of a high inclined satellite generally requires that a large number (e.g., 96) of satellite positions in terms of azimuth and elevation be stored in the park table over a sidereal day, a relatively large memory is required. Third, after a stationkeeping move, the park table data becomes invalid.
A second method used to follow the satellite during times when no tracking information is available is known as parameter tracking and requires a mathematical model of the satellite motion based on parameters obtained from a remote site. The INTELSAT eleven parameter model is an example of this method. This method works well, but it requires a model and the model parameters must be updated regularly for normal satellite motion and stationkeeping moves. A detailed description of the INTELSAT eleven parameter model may be found, for example, in Chang et al., "Inclined Orbit Satellite Operation in the INTELSAT System," INTELSAT, Washington, D.C. (1991).
A third method used to follow the satellite during times when no tracking information is available requires an algorithm which computes parameters for an orbital model from satellite position data. This method can be implemented using park table data. However, if the algorithm uses a park table, it still has the disadvantage of requiring a relatively large memory. In fact, additional memory is required to store the model parameters.
Accordingly, there is a need for a method of accurately tracking an inclined satellite during times when no tracking information is available and which does not require a large memory.